# Bars and rod

Classical Mechanics Level pending

Bars and rod

Two cylindrical horizontal bars are fixed one above the other; the distance between the axes of the bars is $$\ 4d$$, where $$\ d$$ is the diameter of the rod. Between the bars, a cylindrical rod of diameter $$\ d$$ is placed as shown in Figure (this is a vertical cross-section of the system). The coefficient of friction between the rod and the bars is $$\ µ = 1/2$$. If the rod is long enough, it will remain in equilibrium in such a position. What is the minimal length $$\ L$$ of the rod required for such an equilibrium?

You can express your answer in the form $$\ L=xD$$, where $$\ x$$ is a positive, real number. Find $$\ x$$.

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